Comparison of Several Reference Evapotranspiration Methods for Itoshima Peninsula Area, Fukuoka, Japan

Transcription

1 Memoirs of the Faculty of Engineering, Kyushu University, Vol. 66, No.1, March 6 Comparison of Several Reference Evapotranspiration Methods for Itoshima Peninsula Area, Fukuoka, Japan by Othoman ALKAEED *, Clariza FLORES **, Kenji JINNO*** and Atsushi TSUTSUMI**** Abstract Six reference evapotranspiration (ET o ) methods are compared, based on their daily performances under the given climatic condition in the western region of Fukuoka City. The Penman-Monteith equation standardized by the Food and Agriculture Organization (FAO56-PM) is used to compare with the Thornthwaite, Hargreaves, and Hamon methods. The FAO56-PM method has also been used as an index for two equations: the solar radiation (R s ) based and net radiation (R n ) based equations, which are the simplified versions of FAO56-PM. Performance analysis for the calculated values using meteorological data for 7 years (Jan 1996 Dec ) was made. The standard error of estimates (SEE) was calculated on monthly basis. The estimated values by the Thornthwaite, Hargreaves, Hamon, and the R s -based and R n -based radiation methods were all correlated with FAO56-PM having correlation (r ) values calculated by Pearson s correlation of.8,.69,.48,.71 and.45 and their standard error estimates were.5,.5,.5,.8 and.4 mm mon -1, respectively. Proximity in ET o estimates by the Hargreaves and the R s -based methods showed that the solar radiation as input variable was important as the FAO56-PM method. Also, the Thornthwaite method, which uses only temperature as input variable, has been found to have highly correlated with the FAO56-PM method. Thus, when considering the availability and reliability of the input data, the use of all these methods are suggested as practical methods for estimating ET o if the standard FAO56-PM equation is not applicable due to the complexity of its input parameters. Keywords: Reference evapotranspiration by FAO56-PM, Crop evapotranspiration, Water budget estimation, Crop coefficient, Automated Meteorological Data Acquisition System (AMeDAS) * Graduate Student, Department of Urban and Environmental Engineering ** Postdoctoral, Department of Urban and Environmental Engineering *** Professor, Institute of Environmental Systems **** GEOSCO

2 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI 1. Introduction Efficient consumption of groundwater as agricultural irrigation, drinking water and wineries is an important issue in Itoshima Peninsula, the western region of Fukuoka City, Japan, where a new campus of the Kyushu University is under construction. It is anticipated that the construction of the new campus could reduce the groundwater flow toward the residential area, unless appropriate countermeasures are taken. Evapotranspiration (ET) is the loss of water to the atmosphere by the combined processes of evaporation from the soil and plant surface and transpiration from plants 1). Estimation of evapotranspiration is one of the major hydrological components for determining the water budget and is becoming indispensable for the calculation of a reliable recharge and evaporation rate for the groundwater flow analysis. It is therefore, reliable and consistent estimate of evapotranspiration is of great importance for the management of water resources efficiently. Quantification of referable reference evapotranspiration (ET o ) for short grass is necessary in the context of many issues, for example, crop production, management of water resources, scheduling of irrigation, evaluation of the effects of changing land use on water yields, and environmental assessment ). In the neighboring area including the new Kyushu University campus, groundwater is consumed for greenhouse by 7 m 3 d -1, for houses by 4 m 3 d -1, and a few 1 m 3 d -1 for wineries. However, with the construction of the new Kyushu University campus, it is anticipated that this may cause the reduction in the groundwater flow toward the residential area unless proper groundwater management measures are considered. Besides, the urbanization in the surrounding area may also induce the potential effect on the local hydrologic cycle in the future. Thus, the water budget analysis is indispensable for the surface runoff and groundwater flow analyses. It is in this regard that the reliable and consistent estimates of evapotranspiration have to be investigated in order to understand the characteristics of the water movement in the new campus as well as the surrounding area. Tsutsumi et al. (4) applied the Thornthwaite method in order to estimate the monthly crop evapotranspiration (ET c ) in the study area based on the measured mean monthly temperature. However, uncertain estimate with this method in winter gave relatively small values. Therefore, it is worthwhile to examine the other methods to compare with the obtained values by the Thornthwaite method in this area. Kondo et al. (199) presented ET c particularly in the forestry area of Japan using the heat balance-bulk method. They showed the method which includes the effect of transpiration and direct evaporation of the intercepted rainfall of the forest canopy. As a result, the crop evapotranspiration from the forest in Fukuoka area accounted for 86 mm yr -1 in 199. It should be notified that the method developed by Kondo et al. (199) is useful because the rainfall interception can be evaluated in their approach and applicable for the subsequent estimation of the rainwater infiltration and surface runoff components 3), 4). It is obvious that the estimation of rainfall interception is important for the assessment of the possible effect of deforestation on the regional hydrologic cycle. Based on the Thorthwaite s method, Tsutsumi et al. (4) proposed a scheme to estimates the spatial distribution of the ET c by coupling the conventional rainwater infiltration model with the groundwater flow analysis in the study area. They found that the mean special ET c over the study area was 831 mm yr -1 in However, the ET c calculated by the Thorthwaite method gave remarkable inconsistent vales in winter. Since direct measurement of referable ET o for short grass is difficult, time consuming and costly, the most practical approach would be to estimate ET o from climatic variables, such as solar radiation, air temperature, wind speed, and relative humidity. In connection with, various methods are available for

3 Comparison of Several Reference Evapotranspiration Methods 3 estimating ET o, involving equations ranging from the most complex energy balance method requiring detailed climatological data (Allen, 1989) to simpler method requiring less data (Hargreaves, 198; Samani, 1985). Among them, the FAO-56 based on the Penman-Monteith (PM) method (Allen et al., 1998) is currently used and is considered to be a standard method 8). However, the major drawback of FAO56-PM method is that this method requires air temperature, relative humidity, wind speed, and solar radiation which could not be easily available in many meteorological stations particularly in a given location where quality of data and difficulties in gathering all of the necessary weather parameters can present serious limitations 9). Additionally, it also uses the complicated unit conversions and lengthy calculations 1). On the other hand, the Thornthwaite method is considered to be a popular method since it only requires monthly average air temperature. Mintz and Walker (1993) stated that the Thornthwaite method was developed for temperature measured under potential conditions and it only represents the potential evaporation when there is no soil moisture stress. Hence, this method tends to overestimate the potential evaporation in arid regions if air surface temperature is applied. The Hargreaves method is also quite simpler that requires only two climatic parameters: the temperature and incident radiation. This method has been tested using some high quality lysimeter data and broad range in climatological conditions (Hargreaves, 1994) whose results revealed as nearly accurate as PM in estimating ET o. Therefore, the use of the Hargreaves method is recommended in cases where reliable data are lacking. The Hamon method is also considered as one of the simplest estimates of ET o 13), and applicable to estimate seasonal (monthly) or annual values. Haith and Shoemaker (1987) stated that the Hamon method is applicable easily since it requires only average number of daylight hours per day and saturated vapor pressure. Irmak et al. (3) simplified the FAO56-PM method by expressing a multi-linear regression function which requires less input parameters and computation. This uses only the solar radiation (R s ), net radiation (R n ) and mean daily temperature (T m ) as input parameters to estimate the ET o. Although, many approaches have been developed and adapted for various applications based on available input data, there is still a remarkable range of uncertainty related to which method is to be adopted specifically in the calculation of reference evapotranspiration for short grass at a given area. Thus, for the purposes of establishing a common method which can provide a more accurate ET o estimation, these estimation methods were researched on the basis of their variability in input variables. The performances of these methods were evaluated and compared with the FAO56-PM for estimating the ET o particularly at the new Kyushu University Campus area whose meteorological properties are characterized as having high humidity and heavy precipitation. Besides, the crop coefficient for the forest canopy was discussed through the comparisons of the presented values for the forest in the Fukuoka areas with the reference values calculated by the above six methods.. Methodology.1 Study area and climatic characteristics Figure 1 shows the study area (Itoshima peninsula) including new campus of Kyushu University, located in the northern part of Kyushu Island, western region of Fukuoka City, Japan, latitude 33 o 5 to 33 o 4 N, longitude 13 o 7 3 to 13 o 16 E.

4 4 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI Fig. 1 Study area (Itoshima). The total area of Itoshima is about km. The climate in the area is characterized as having high humidity, high wind speed, and heavy precipitation. The meteorological data in the present study were obtained from the Maebaru Automated Meteorological Data Acquisition System (AMeDAS) station in Maebaru City, Fukuoka, Japan, which is close to the new Kyushu University Campus, (latitude 33 o N, longitude 13 o 11 3 N) within an agricultural area. The average annual precipitation is 1646 mm yr -1 (1996-), approximately more than 5% of which occurs in June-August. Air temperature ranges from 19. o C and 31.1 o C in summer and 1.7 o C and 15.4 o C in winter months. Daily mean temperature in summer is 3.3 o C and 9.6 o C in winter. On the other hand, daily mean minimum and maximum relative humidity are 37% and 9% with annual average of 67%, respectively. The observed maximum and average daily wind speed in this period were 4.5 m s -1 and.8 m s -1 3).. Equations..1 The (FAO56) Penman-Monteith equation The (FAO56) Penman-Monteith equation for predicting ET o where applied on 4-h calculation time steps has the form: ET o.48δ( R = n 9 G) + γ u ( e T + 73 Δ + γ (1 +.34u ) s e a ) (1) Where ET o is reference evapotranspiration [mm day -1 ], R n is net radiation at the crop surface [MJ m - day -1 ], G is soil heat flux density [MJ m - day -1 ], T is mean daily air temperature at m height [ C], u is wind speed at m height [m s -1 ], e s is saturation vapour pressure [kpa], e a is actual vapour pressure [kpa], e s -e a is saturation vapour pressure deficit [kpa], Δ is slope vapour pressure curve [kpa C -1 ], and γ is psychrometric constant [kpa C -1 ]. In application having 4-h calculation time steps, G is presumed to be and e s is computed as

5 Comparison of Several Reference Evapotranspiration Methods 5 e ( Tmax ) + e ( Tmin ) e s = () Where e ( ) is the saturation vapor function and T max and T min are the daily maximum and minimum air temperature. The FAO Penman-Monteith equation predicts the evapotranspiration from a hypothetical grass reference surface that is.1 m in height having a surface resistance of 7 s m -1 and albedo of.3. The equation provides a standard to which evapotranspiration in different periods of the year or in other regions can be computed and to which the evapotranspiration from other crops can be related. Standardized equations for computing all parameters in Eq. (1) are given in Allen et al. (1994ab, 1998) or Smith et al. (1991), 15)... Thornthwaite equation The Thornthwaite equation given by (Thornthwaite, W. 1948) is a 1Ti N 1 ET = 16 (3) I 1 3 I = 1 T i 1 i= (4) 3 6 ( I 771I ) 1 a = I (5) where, T i is the mean monthly temperature [ C], N is the mean monthly sunshine hour. The main advantage of this method is that only the temperature information is needed besides the sunshine hours. Generally, it is known that the Thornthwaite method gives the underestimate in the arid area while the overestimate in the humid area, respectively...3 Hargreaves equation The Hargreaves et al. (1985) equation is expressed as ET o ( T m )( Tmax Tmin ) R a =.3 (6) where T m is daily mean air temperature [ C], T max is daily maximum air temperature [ C], T min is daily minimum air temperature [ C], and R a is extraterrestrial radiation [MJ m - day -1 ]. The mean air temperature in the Hargreaves equation is calculated as an average of T max and T min and R a is computed from information on location of the site and time of the year. Therefore air temperature is the only parameter that needs to be measured continuously in order to use Eq. (6) 17)...4 Hamon equation The Hamon equation given by (Haith, D. A. and Shoemaker, L. L., 1987) is expressed as.1 H t es ET = (7) o ( T + 73.) mean where H t [day] is average number of daylight hours per day.

6 6 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI..5 Solar radiation (R s ) based method (Irmak et al., 3) ET = R +. 79T (8) o s mean where R s [MJ m - day -1 ] is solar shortwave radiation...6 Net radiation (R n ) based method (Irmak et al., 3) ET = R +. 3T (9) o where R n [MJ m - day -1 ] is net radiation. n mean.3 Climatic parameters required by each equation One of the important considerations in establishing a simple method other than the standard method such as the FAO56-PM is the high possibility of unavailability and unreliable weather data measurement and collections. In general, a setup of the devices for the meteorological measurement at the remote areas and at a given location is difficult. With this given scenario, accuracy of data, specifically the data of advanced input variables such as humidity and radiation would be low. Table 1 shows the data requirements for the FAO56-PM, Thornthwaite, Hargreaves, Hamon, and R s -based and R n -based equations, respectively. Table 1 Comparison of each method in terms of the number of parameters required. method FAO56-PM Thorthwaite Hargreaves Hamon R s -based radiation variables R n -based radiation temperature necessary necessary necessary necessary necessary necessary humidity necessary necessary necessary wind speed necessary radiation necessary - necessary - necessary necessary no. of daylight hours - necessary - necessary necessary necessary saturated vapour pressure necessary Results and Discussions 3.1 Climatic data The meteorological data of 7 years at the Maebaru AMeDAS station covering the period of January December were analyzed for purposes of calculating evapotranspiration by the different methods. Figure shows the daily precipitation, temperature, wind speed, relative humidity, solar radiation and net radiation data used for ET o estimations. The daily solar radiation and net solar radiation were plotted in Fig (e) and Fig. (f). They were calculated by the procedures which are presented in the FAO56-PM estimation 1). These variables are important for the calculation of ET o as required in the FAO56-PM estimation. The relationship between solar radiation and net solar radiation depicts the same trend in all years wherein the total solar radiation is doubled of that in the net radiation.

7 Comparison of Several Reference Evapotranspiration Methods 7 Precipitation (mm d -1 ) a Average temperature ( o C) Time (day) Time (day) d Wind speed (m s -1 ) Relative hum idity (% ) 1 Solar radiation (MJ M d -1 ) b 1 5 d e Time (day) Time (day) 1 8 c 15 f Time (day) Time (day) Net radiation (MJ m d -1 ) 35 Fig. Input parameters used in the calculation of ET o by different ET o estimation methods (a) precipitation [mm day -1 ]; (b) relative humidity [%]; (c) wind speed [m s -1 ]; (d) average temperature [ o C]; (e) solar radiation [MJ m - day -1 ]; and, (f) net solar radiation [MJ m - day -1 ], respectively. The 7 year-daily weather data were used to validate the performances of the commonly used ET o estimation methods. Comparison of monthly ET o values specifically for the Thornthwaite, Hargreaves, Hamon, R s -based and R n -based equations and are presented in Fig. 3.

8 8 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI FAO56 PM ETo (mm mon -1 ) a Time (mon) Hamon ETo (mm mon -1 ) 175 d Time (mon) Thornthwaite ETo(mm mon - 1 ) b Time (mon) Rs ETo (mm mon -1 ) e Time (mon) Hargreaves ETo (mm mon -1 ) c Time (mon) Rn ETo (mm mon -1 ) f Time (mon) Fig. 3 Estimated ET o derived from different methods: (a) FAO56-PM (b) Thornthwaite (c) Hargreaves (d) Hamon (e) R s -based method (f) R n -based method. Unit is [mm mon -1 ]. Although the trends of the estimated ET o are in proximity among the applied methods, it is surprising that none of the methods show the same results. Seasonal variations in the ET o estimation reflect the differences in the variables applied in each method. Figure 4 shows the comparisons of annual ET o estimations. In the present calculations, the annual sum of ET o estimations based on the solar radiation as input variable showed the highest value among the tested methods having the values ranged from 957 mm yr -1 in mm yr -1 in in R s -based method, while 184 mm yr -1 in mm yr -1 in 1 for R n -based method, respectively. The ET o estimations by the Hamon method has the lowest values ranged from 831 mm yr -1 in mm yr -1 in 1998 whereas the Thorntwaite method is very close with the FAO56-PM having the values ranged from 845 mm yr -1 in mm yr -1 in 1998, respectively. The low ET o values obtained by the Hamon and Thornthwaite methods having 831 mm yr -1 and 845 mm yr -1 both in 1996 were found to be close with the ET o estimations reported by Kondo (199) et al. and Tsutsumi et al. (4) of 86 mm in 199 and 831 mm in 1996 for Fukuoka area.

9 Comparison of Several Reference Evapotranspiration Methods 9 FAO56Penman Thornthwaite Hargreave Eto Rs Eto Ra Hamon 14 1 Total ETo (mm yr -1 ) Time (year) Fig. 4 Total annual evapotranspiration estimates given by the different methods covering the 7 year meteorological data obtained from the Maebaru AMeDAS station, Fukuoka, Japan. Comparisons of the Thornthwaite, Hargreaves, Hamon, and the R s - and R n - based methods were all correlated with FAO56-PM having r values, which can be calculated using Pearson s correlation (STATSOFT, Statistica, 1999 Edition), of.8,.69,.48,.71 and.45 as shown in Fig. 5, respectively. Results of the ET o estimations by the Hargreaves and R s -based methods, which use the solar radiation, and the Thornthwaite method by temperature as input variable, were found to be significantly correlated with the ET o estimation by the FAO56-PM. This fact implies that these input variables are significant for obtaining the proximate values in the ET o estimations. When considering the availability and reliability of the input data, the use of these methods are suggested as practical methods for estimating ET o, if the standard FAO56-PM equation can not be used due to the complexity of its input parameters. 3. Comparison of the performance of different methods relative to FAO56-PM The performances of the tested methods were analyzed by computing the standard error of estimate SEE of the monthly ET o between the FAO56-PM and other methods. The SEE is computed following the equation presented by Irmak et al. (3) as: 1 { n( n ) } n n yi i= 1 n yi i= 1 n n n n x i yi ( xi ) ( yi ) i= 1 i= 1 i= 1 n n n x i xi i= 1 i= 1 SEE = (1) where x i ; ET o estimated using the FAO56-PM (mm mon -1 ) y i ; ET o estimated using other equations (mm mon -1 )

10 1 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI n i; sample size The lower SEE implies the better performance of the applied method. Table and Fig. 5 show the calculated average SEE on the monthly basis for all the methods indicating the low values such as.5,.5,.5,.8 and.4 mm d -1 for the Thornthwaite, Hargreaves, Hamon, R s and R n -based methods, respectively. The calculated SEE for all the methods shows almost the same values reflecting good performances as manifested for all the calculation years. The average ratio above and below 1. for different methods indicates over- and underestimation of ET o relative to FAO56-PM method. As shown in Table, the average ratio defined as the ratio of ET o method to ET o FAO56-PM gave the values of.89, 1.1, 1.13 and 1.3 and.94 for the Thornthwaite, Hargreaves, Hamon, R s and R n -based methods, respectively. Among the methods, the Hargreaves, Hamon, and R s -based methods resulted in the overestimation of ET o relative to the FAO56-PM method. The high correlation of ET o by the Hargreaves and R s -based methods with FAO56-PM method clearly reflects the importance of the incident solar radiation as they are calculated by using the temperature and solar radiation. This fact is also supported by many studies which reveal that the Hargreaves method is nearly as accurate as the FAO56-PM method in estimating ET o. Therefore, it could be recommended to use the Hargreaves method in the case of which other reliable data are lacking 1). However, it should be notified, as Temesgen et al. (1999) have indicated, that high humidity conditions may result in an overestimation of ET o by the Hargreaves method whereas the conditions with high wind speed may result in the underestimation of ET o. Moreover, the performance of the RB s -based method developed with the aim of simplifying the calculation and input variables for the FAO56-PM method performed well and its estimations of daily, monthly and annual ET o are close to the estimates obtained by the FAO56-PM method. Additionally, the comparisons made for all the methods signifies that all these methods can be successfully used to estimate the ET o specifically in areas having the same climatic conditions as the one presented in this study.

11 Comparison of Several Reference Evapotranspiration Methods 11 Table Standard Error of Estimates (SEE) in mm mon -1 of ET, Average Ratio of ET method / ET o FAO56-PM of the commonly used methods for estimating ET covering the years year Performance indicator Thornthwaite Hargreaves Hamon R s R n 1996 SEE of monthly estimate Average ratio SEE of monthly estimate Average ratio SEE of monthly estimate Average ratio SEE of monthly estimate Average ratio SEE of monthly estimate Average ratio SEE of monthly estimate Average ratio SEE of monthly estimate Average ratio Average SEE of monthly estimate Average ratio

12 1 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI Thornthwaite ET (mm mon -1 ) o a y = *X r = R s ET o (mm mon -1 ) d y = *X r = FAO 56 PM ET o (mm mon -1 ) FAO 56 PM ET o (mm mon -1 ) Hargreaves ET (mm mon -1 ) o b y = *X r =.69 R a ET o (mm mon -1 ) e y = *X r = FAO 56 PM ET o (mm mon -1 ) FAO 56 PM ET o (mm mon -1 ) o (mm mon -1 ) c y = *X r =.48 Hamon ET FAO 56 PM ET o (mm mon -1 ) Fig. 5 Regression analysis for the ET o estimates of (a) Thornthwaite (b) Hargreaves (c) Hamon (d) R s -based method (e) R n -based method with FAO56-PM for evaluation years of at Maebaru, Fukuoka, Japan. Unit in (mm mon -1 ) and n = Conclusions The 7-year meteorological data derived from Maebaru AMeDAS station and Fukuoka local meteorological station located in Fukuoka Japan was applied as input parameters for comparing different methods to estimate ET o under existing climatic conditions in Fukuoka, Japan. The major drawback is that the real ET o is unknown however, numerous studies have been performed wherein the FAO56 PM method have shown to be the best method for estimating ET o in which the calculated ET o values correspond to lysimeters and other precise devices where real ET o can best obtained. The performances of the Thorthwaite, Hargreaves, Hamon, R s -based and R n -based equations for monthly ET o estimates and are significantly correlated with the ET o estimates in FAO56-PM method although the Thorthwaite method was found to have highly significant estimates. Among the methods used, only the Thorthwaite method requires temperature as the only input parameter whereas other methods used radiation input to estimate the ET o. These approaches require only few parameter inputs thus making it more dynamic for the

13 Comparison of Several Reference Evapotranspiration Methods 13 application in the area when the accuracy in weather measurement is less expected as compared with complex data input required by FAO56-PM approach. Thus, these methods could be used as a potential method to estimate ET o. In conclusion, it can be emphasized that the use of the FAO56-PM as a standard method remains the most desirable method for estimating ET o if accuracy of data collection is considered to be the main consideration. But in many cases especially in areas where accurate data collection is difficult, the application Hargreaves and R s -based equation could be utilized for accurate and consistent estimates of daily ET o relative to the FAO56-PM method especially in humid climate like in Japan is to be considered. Alternatively, reliable ET o estimates derived from Thornthwaite method can be used to calculate the ET o when temperature is the only input parameter available. However, the differences in the ET o estimates using these methods have provided a significant range of uncertainty. It is therefore important to compare and validate these methods based on the precise evaluation considering the land coverage and topographical condition. References 1) Allen, G. R., Pereira, L. S., Raes, D and Smith, M Crop Evapotranspiration-Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56. FAO, Rome, Italy, ) Sharma, M.L., Estimating evapotranspiration. Advances in irrigation. D. Hillel, ed., Academic, London, ) Tsutsumi, A., Jinno, K. and Berndtsson, R. 4. Surface and subsurface water balance estimation by the groundwater recharge model and a 3-D two-phase flow model. Hydrological Sciences Journal. 49(), ) Kondo, J., Nakazono, M., Watanabe, T., and Kuwagata, T Hydrological climate in Japan (3) Evapotranspiration from forest. Japan Society of. Hydrology & Water Resources, Vol. 5, No. 4. 5) Allen, G. R., Jensen, Marvin. E., Wright, James. L., and Burman, Robert. D., Operational estimates of reference evapotranspiration. Agronomy journal. Vol. 81, ) Hargreaves, G. H., and Samani, Z. A Estimating potential evapotranspiration. Journal of Irrigation Drainage Engineering, 18(3), ) Hargreaves, G. H., and Samani, Z. A. 1985: Reference crop evapotranspiration from temperature. Applied Engineering Agric., 1: ) Walter, I. A., Allen, R. G., Elliott, R., Mecham, B., Jensen, M. E., Itenfisu, D., Howell, T. A., Snyder, R., Brown, P., Eching, S., Spofford, T., Hattendorf, M., Cuenca, R. H., Wright, J. L., and Martin, D.. ASCE Standardized reference rvapotranspiration equation. In:Evans RG, Benham BL, Trooien TP (eds.) Proc. National Irrigation Symposium, ASAE, Nov ,, Phoenix, AZ. pp ) Irmak, S., Irmak, A., Allen, R.G., and Jones, J. W. 3. Solar and net radiation-based equations to estimate reference evapotranspiration in humid climates. Journal of Irrigation and Drainage Engineering. ASCE. 19(5): ) Wu, I A simple evapotranspiration method for Hawaii: the Hargreaves method. Engineer s Notebook 16. College of Tropical Agriculture & Human Resources (CTAHR) Fact Sheet, ) Mintz, Y., and Walker, G. K Global fields of soil moisture and land surface evapotranspiration derived from observed precipitation and surface air temperature. Journal of

14 14 O. ALKAEED, C. FLORES, K. JINNO and A. TSUTSUMI Applied Meteorology, 3, ) Hargreaves, G. H., Defining and using reference evapotranspiration. Journal of Irrigation and Drainage Engineering, ASCE 1(6): ) Hamon, W. R., Estimating potential evapotranspiration. Journal of the Hydraulics Division, ASCE. 87(HY3): ) Haith, D. A., and Shoemaker, L. L Generalized watershed loading functions for stream flow nutrients. Water Resources Bulletin, 3: ) Allen, G. R.,. Using the FAO-56 dual crop coefficient method over an irrigation region as part of an evapotranspiration intercomparison study. Journal of Hydrology ) Thornthwaite, C. W An approach toward a rational classification of climate. Geography. Rev ) Temesgen, B., Eching, S., Davifoof, B., and Frame, K. 5. Comparison of some reference evapotranspiration equations for California. Journal of Irrigation and Drainage Engineering. ASCE (5) 131:1 (73).